A revisit to Bennett’s goodness-of-fit statistic for comparing two predictive values

Abstract

Bennett (Statistics in Medicine 4 (1985), 535-539) proposed a goodness-of-fit statistic to compare two predictive values in an attempt to improve upon its earlier version he derived in 1976. However, this new version of Bennett’s goodness-of-fit statistic was not presented correctly, and more importantly, its validity has been questioned by several authors in the literature as it did not involve the disease prevalence, a part of the two Predictive Values to be compared. To shed some light on this classical test statistic, in this paper, we first obtain the corrected version of Bennett’s goodness-of-fit statistic. We then compare the corrected version with its recent Wald counterpart proposed by Wang (Statistics in Medicine 25(2006), 2215-2229) and show that the two statistics are asymptotically equivalent. The validity of the corrected Bennett’s goodness-of-fit statistic is further supported by a simulation study which indicates that Bennett’s goodness-of-fit statistic with correction has similar finite sample performance to its Wald counterpart. In conclusion, the corrected Bennett’s goodness-of-fit statistic is a competitive statistic for testing equality of two predictive values.

Keywords:

• Predictive values
• Bennett’s goodness-of-fit statistics
• Wald statistics
• asymptotic equivalency

Acknowledgments

I would like to thank three anonymous referees for their valuable comments that resulted in an improved version of this paper.